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SMM/TMP based F-statistics

 

As with the distance methods, all of the above methods of estimating are based on the assumptions of the IAM, i.e. no homoplasy. Slatkin (1995) has shown that the measures of average sum of squares of the difference in allele size are related to . From coalescent theory it can be shown that is related to the average coalescence times, such that,

where is the average time to coalescence of any two randomly chosen alleles from the entire population, and is the average time to coalescence of any two randomly chosen alleles drawn from the same subpopulation (Slatkin 1991). In two populations with divergent alleles, the average time to a common ancestor for any two alleles in a subpopulation is going to be less than the average time to coalescence of any 2 alleles drawn from the entire population. Based on this relationship, Slatkin (1995) developed an estimation of that would incorporate the mutational history contained within the alleles under the SMM, .

Where and are the average sum of squares of the difference in allele size within a subpopulation and the entire population as describe above. Slatkin noted that the and that the . Thus,